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Chapter 0: Problem 110

Explain how to simplify \(\sqrt{10} \cdot \sqrt{5}\)

Short Answer

Expert verified
The simplified form of \( \sqrt{10} \cdot \sqrt{5}\) is \(5 \sqrt{2}\).

Step by step solution

01

Apply the multiplication property of radicals

Write \(\sqrt{10} \cdot \sqrt{5}\) as the square root of their product, \( \sqrt{10 \cdot 5}\).
02

Calculate the product

Calculate \( 10 \cdot 5 \) which equals 50. So now we have \( \sqrt{50}\).
03

Simplify the square root

The number 50 can be factored into 25 and 2, where 25 is a perfect square, so \( \sqrt{50} \) becomes \( \sqrt{25 \cdot 2} \).
04

Further simplify the square root

Since the square root of 25 is 5, \( \sqrt{25 \cdot 2}\) simplifies to \( 5 \sqrt{2} \).

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